Variational Quantum Algorithms as Hybrid Control Systems
An interactive thesis exploring optimization dynamics in variational quantum algorithms—separating the quantum substrate from the classical controller.
Chapters
Why VQAs should be analyzed as hybrid control systems, and what this lens explains.
Parameterized states, observables, measurement, and how the objective landscape is induced.
Mapping circuits + estimators + optimizers into a closed-loop system model.
Why non-gradient dynamics matter under noise, nonconvexity, and sampling.
The proposed controller, dynamics, constraints, and design rationale.
Stabilizing objectives and controllers; linking bias–variance to control robustness.
What this viewpoint changes: benchmarking, design rules, and future directions.
Appendices
Jordan–Wigner and Bravyi–Kitaev mappings, Pauli decomposition, qubit requirements.
Pauli term grouping, commuting cliques, shot budgets, and estimator variance.
Statevector vs shot-based simulation, depolarising noise, and how noise enters the optimization loop.